8. Advanced Topics

• 8.1. Objectives
• 8.2. Python Lists Revisited
• 8.3. Recursion Revisited
  • 8.3.1. Modular Arithmetic Theorems
  • 8.3.2. Modular Exponentiation
  • 8.3.3. The Greatest Common Divisor and Multiplicative Inverses
  • 8.3.4. RSA Algorithm
• 8.4. Dictionaries Revisited: Skip Lists
  • 8.4.1. The Map Abstract Data Type
  • 8.4.2. Implementing a Dictionary in Python
    • 8.4.2.1. Searching a Skip List
    • 8.4.2.2. Adding Key-Value Pairs to a Skip List
    • 8.4.2.3. Building the Map
    • 8.4.2.4. Analysis of a Skip List
• 8.5. Trees Revisited: Quantizing Images
  • 8.5.1. A Quick Review of Digital Images
  • 8.5.2. Quantizing an Image
  • 8.5.3. An Improved Quantization Algorithm Using Octrees
• 8.6. Graphs Revisited: Pattern Matching
  • 8.6.1. Biological Strings
  • 8.6.2. Simple Comparison
  • 8.6.3. Using Graphs: Finite State Automata
  • 8.6.4. Using Graphs: Knuth-Morris-Pratt

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